It’s not that they wouldn’t be possibilities but that the probability of admission is still likely to be low. He should be well placed instate for UCB/UCLA (especially as math is in L&S which is an easier admit), but the chance of getting into Oxbridge is significantly higher than the chance of getting into the Ivies or Stanford. IIRC @HazeGrey ‘s S applied to some Ivies.
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Just wanted to chime in here as I also have what people refer to as a “pointy” math kid. Most of his ECs revolve around math though he is also a runner and has participated in that throughout high school. He applied to brown ED and was accepted. He chose brown for his ED over more STEM focused schools because he wanted a more diverse (with regard to major/interests) and less competitive (more collaborative) student body and really loved brown’s open curriculum and overall vibe. His whole life he has said that MIT was his dream school (largely because that’s what people told him it should be), but in the end he surprised us all with his choice. Hope your son finds his fit.
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Math acceleration would be noted especially if it’s not forced, which I don’t think your son’s is. Taking classes at Berkeley is not the same as taking classes in the summer so you can take Calculus as a senior, which is the typical acceleration.
Unless we get some idea of affordability, whatever you’re comfortable sharing, it’s hard to give advice. Early decision could help your son at some colleges but you have to be ok that it’s binding from a financial side.
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About math acceleration, my S21 was accelerated (AP Calc in elementary school) and did some competitions (respectable AIME level, never made it to USAMO) and residential math summer programs. He reports that practically all of his buddies from the summer programs are already in early at MIT, Harvard, Yale, Stanford and a number of others. He said he knew about 15 in early at MIT alone just from one summer camp. My S21 was also accepted SCEA at a T5 school.
The point is that much is made of the competition at the T20 schools and I am not going to downplay that. But by the same token, there are really not that many kids like this, as the numbers show. I think the advice to follow your interests as deeply as possible makes sense, and if my anecdotal experience is worth anything, OP’s son might be pleasantly surprised come college admission time.
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I don’t know that I’d agree that your son wouldn’t be valued by top US schools. My observation is that the most selective and academically rigorous colleges, especially midsized and small privates, DO appreciate intense focus – passion, if you will –
in the applicants’ areas of interest, both academic and extra-curricular as well as diversity of life experiences. Whether that appreciation translates into advanced/accelerated placement really depends on the individual college and specific department.
I think “well rounded” is a phrase that has seen better days, but again my observation, applicants that can offer more than one thing probably have a leg up in admissions, especially at smaller colleges which need to fill spots on sports teams, orchestras, theaters etc. To me, in light of your son’s exceptional academic profile, his extracurricular interests in piano, cubing, chess would suffice even at the most selective schools. However, he would need to use his essays, recommendations and supplements to flesh out who is and how he would fit with the school’s culture.
“Fit” is a two way street: The colleges need to fit the students’ academic and social requirements and the students need to fit the colleges’ priorities. Large universities have a wide spectrum of both and tend to focus admissions on the applicants’ academic achievements, figuring that the cultural element will sort itself out. Academically rigorous small and medium privates (I hate the descriptor “elite” but I guess that’s the whole point) look to both: Can the applicants handle the work? What will they contribute to the campus community, in and out of the classroom?
From the students’ perspective, of course it’s imperative that the school can offer academics in the discipline and on the level that they require, which in your son’s case, may limit him to a short list of options. But in addition to academic requirements, the applicants (and their parents) also need to evaluate non-academic factors such as size, location, environment and the overarching culture and personality. In essence, Where would they be most happy? Where would they be most likely to succeed? Finding balance between academics and culture is what “fit” is all about.
In other parts of the world, undergraduates can fast track into many career paths, but in the US, there are few professional terminal degrees on the undergraduate level: engineering, architecture, nursing for example. For law, medicine, college level teaching and many other career paths advanced degrees are required or at least commonly recommended. We can argue all day and night whether core curriculums and/or distribution requirements provide a beneficial foundation or are a waste of time. Though I personally consider the undergraduate opportunity to study a range of disciplines with experts in the field one of the great beauties of a liberal arts education, I wouldn’t say that one system is better than the other, just different.
The four years of undergraduate education are truly formative periods, not only intellectually but also in many other aspects of a person’s development. Your son will meet people and make decisions that will influence the rest of his life.
At this point in your son’s search I think you are wise to keep his options open. He has certainly demonstrated that he loves pure math and that he can succeed in a demanding academic environment, but beyond that he’s still a 16/17 year old with a lot of room for intellectual and social development ahead of him. When you drop him off at his dorm room in September 2022 he may still be a “shy kid” who wants to stay near home and to study math and only math, or maybe not. As you said, he may surprise you.
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@beekmom, I understand that admission data at Harvard, the one place they’re more or less out in the open now, show that a small percentage of students (I have heard roughly 10 percent mentioned) is being admitted more or less on their academic chops alone, just as most recruited athletes are admitted mostly on their ability to play ball.
While it’s of course mostly the grad school that produces professors, they do want some Harvard undergrads in that cohort.
As such, your kid would be valued and his chances at admission at those T20s that admit the rest of the class by holistic criteria are not really affected by those criteria not fitting him well.
However. I think we can all agree that a kid that knows at the age of 16 that he wants to do pure math and nothing but is not really a good fit for the the US system as such, because the system as a whole doesn’t value that kind of focus.
The UK system does, more than most. (Most countries in the rest of the world demand breadth until high school graduation at 17-19, with some narrowing of focus for the last two years or so - the UK, specifically England, does not). Oxford and Cambridge math departments would be full of his peeps, with Cambridge a bit more mathier. (You’ll get loads of pre professional students, too, particularly PPE at Oxford, and linguists and musicians and historians and what all for variety, and the college system makes sure you don’t need to stay in your own bubble socially unless you want to, but your academics will be all math.
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Cont. (Sorry, the site is glitchy for me today).
That said, there are many reasons for a student and their family to not want to go overseas. A certain pandemic comes to mind, of course, but also the demands for independence, the lack of handholding particularly as compared to US LACs (yup, I stand by that!), financial reasons, and, specifically for the UK, the Brexit disaster hasn’t even had its full impact yet.
Which is why I advocated checking out the Williams at Exeter options, to combine the best of what a US LAC and Oxford have to offer, and others suggested the Amherst/UMass combo. Also, smaller research universities with not-too-onerous distribution requirements can work - but he will remain a fish out of water in the US system, that’s for sure.
But I think this thread has thrown up a great many suggestions that together make up a tentative list, and a way forward!
For Oxford and Cambridge, he can, in a way, apply to both! 
Get that complement of three AP 5s in math and science together (@twoin18, is it three or five for Cambridge? I forget), then prepare for sitting the STEP papers. He might love it! A great result might make Cambridge a safety, ROFL, and with an iffy result, he can, as @Twoin18 suggested, still try for Oxford by taking the MAT, which I understand has a lower ceiling.
For the US research Us he needs to make sure he’s got their formal breadth requirements down, such as the 4 years of foreign language and stuff, and keep up the piano for a non math EC to put down, but otherwise I’d assume he can be “unapologetically pointy”, because there is a bucket for that and he fits.
Then there will be a selection of UCs (at least the flagships and CCS at UCSB - graduate studies on the beach, what’s not to like?) with maybe a couple Instagram (what? Autocorrect, are you insane? I put in state!) safeties thrown in there.
The LACs plus options need some more research, I think. Not sure they have a bucket for the “unapologetically pointy” at Amherst and Williams. Maybe Swarthmore (plus UPenn) and Harvey Mudd.
Sorry for the novel! Enjoy your kid, he sounds great!
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Your son certainly has a better than average (which is very low) chance of admission to a US tippy top, but I agree with @Twoin18, his odds of acceptance to Oxbridge is much better. For more STEM-focused schools like MIT/Caltech, there’s a high proportion of their applicants who are on a highly accelerated path in math, so acceleration in itself isn’t an admission “tip”. For schools like Harvard/Princeton, as @Tigerle has pointed out, they do have some small “bucket” for academic “superstar” students. However, they’re likely spread out over many more subject areas (including non-STEM subjects) and few were accepted based on academics alone (if Harvard lawsuit data are any indication). On the subject of math, it’s also fairly clear that these schools, especially MIT/Harvard, favor medalists in math Olympiads, rather than those who had exposures to more advanced math. There’s a comment above on the difference between taking a course at Berkeley and a similar course at a local U (e.g. a CC). Yes, the colleges will view the Berkeley course as more rigorous, but they will also likely consider the issue of accessibility, as they want to be fair to other applicants.
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@BeekMom Since @Twoin18 referenced me/my son, I’ll just share a little of our experience. My Oxford 4th year sounds a lot like your son. Well rounded (state math champ, candidate master chess rating, varsity tennis/skiing) but with a strong math “point”. MIT was his dream school. He was deferred/rejected. Also rejected from Caltech, Yale, Princeton and a courtesy legacy waitlist at Brown. Part of that experience is due to the fact that Ivy admission from his HS is tough because of the number of legacies/recruited athletes they have to place. Another part of it was that once he received his Oxford offer, he told his college counselor that Oxford was his first choice, so I’m not sure how hard they worked to get him in anywhere else RD as it would have taken up one of their slots. Plus they were thrilled to show Oxford on their annual matriculation report.
He liked the “un-holistic” admissions approach at Oxford. He knew that if he got in it was because he had done well on the admissions test and at interview and if he was rejected, it was because he hadn’t.
His college (Worcester) seems to have a large cohort of math students - 15 alone in my son’s year. The director of undergraduate studies at the Mathematical Institute is a tutor there. Definitely a broad spectrum of very talented students, so if your son is looking for that kind of environment, I would seriously consider Oxford and Worcester in particular.
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This aspect contributed to why I listed it 4th (of 20 schools) in my original list. It doesn’t seem that confirming my preceding research either contradicts my information or supports your apparent intent.
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Wholeheartedly agree. These schools are a reach for all. But for some, the chances are better.
We also know many kids from a STEM team kids have been on ( highly competitive, highly ranked). Every year the Seniors land at most Ivies, Caltech, Olin, and MIT. One went to UM ( fincl reasons). They often get accepted ED. Why? High degree of specialization and commitment, IMHO.
Pointy kids are common at top schools. So are well rounded kids.
These pointy math kids are NOT that common in the US. ( This is particularly true if you take out international applicants from boarding schools etc)
Math programs here aren’t designed based on the kids but follow a set path. Advanced kids in public schools often have no options until high school and even then it might be limited. Not every kid has access to or wants to attend college courses so many are self taught or on regional math teams.
It’s actually pretty rare to find these kids. I’d imagine AO’s look at them as potential PHd’s. Lol. Or at least having a small subset of kids deeply involved in a subject. Same goes for anything really.
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Regarding math peers at US universities… Would he eventually find some of them among math graduate students?
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Agreed. It’s supposed to be five 5s for Cambridge, but that’s just a filtering technique to limit the number of applicants, since STEP is usually done after the (conditional) offer not before.
With regard to Brexit, while undoubtedly a negative for the UK economy, it will be a significant help for American applicants next year, because there will be a big drop in European applicants once they have to pay full international fees.
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Regarding your son’s admissions prospects, consider this. Those who have read The Gatekeepers encountered a conversation in which a dean at Wesleyan was asked whether an exceptional physics student would be admitted on this aspect alone. The reply was an unequivocal yes. Since your son shows an equivalent advanced level in his area of interest to that of the hypothetical physics student, his prospects would seem to be good at truly academically oriented schools. Even this basis will be enhanced, in that your son, as you have described him, will not be applying as a strictly one-dimensional candidate.
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I think it’s more likely at small schools than at larger ones, where graduate students are more likely to hold discussions among themselves than with an undergrad who happen to be in their classes.
There was a time when some singular achievement meant an applicant could be assured of a seat at a top college, but that assurance is much less true today, especially at a tippy top.
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An interesting anecdote was from the father of a neighbor (now in his early 80s). He grew up in a poor Appalachian state, and was all set to go to the local state flagship when he won the state math championship. The organizer said hold on a minute, I’ll just call Harvard and get them to offer you a place, which they did (he later became a well known math professor).
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The roster of graduate students in math at Wesleyan can all fit on one page of my laptop screen:
Graduate Students, Mathematics and Computer Science - Wesleyan University
Interesting that the two of you both equate love of learning with breadth of learning. I don’t think it’s the same thing.
Agree it’s a generalization but typically the kids who love learning for the sake of learning like to take a broader, cross-disciplinary approach, maybe to see how diverse topics fit together. Depth would be the more pre-professional track.
“There are many people who love both Shakespeare and STEM.”
They wouldn’t love it at the same level, the student targeting say a high tech job in CS would take a lot of classes that would help in getting one - algorithms, data science etc… and just take the minimum humanities/social science courses to graduate.
Actually, a CS major may have plenty of free elective space in the schedule to take more than the minimum required humanities and social science courses in addition to all desired CS courses. It can depend on how voluminous other requirements at the college are.